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This paper studies the impact of voice traffic on the performance of packet data (PD) transmission in terrestrial trunked radio (TETRA) networks. Particular emphasis is given on the performance of applications characterized by occasionally transmitting small messages between a number of radio terminals and a fixed server while these terminals are also conducting group voice calls. Such applications are constantly increasing in TETRA networks, and so does the need to dimension and configure these networks to meet their reliability, delay, and loss requirements. However, the impact of group voice calls on PD transmission has not been sufficiently studied, and this constitutes the main motivation of our performance analysis. We present simulation results for a variety of practical scenarios, and we discuss how key performance indicators such as PD delay and loss rate are affected by the group call activity of the radio terminals. Our results can help in dimensioning and planning TETRA networks, particularly in determining the number of PD terminals that can be supported in a cell for a given traffic profile and for quality-of-service requirements.